Chapter 11, Problem 1MC

To determine

Whether the given statement “The expression $2\left(x+3\right)$ is equivalent to the expression $2\cdot x+3$” is true or false.

Answer to Problem 1MC

The given statement is false.

Explanation of Solution

Definition used:

Equivalent expressions:

Two expressions that have the same value for all allowable replacements are called equivalent.

Property used:

Distributive law of multiplication over addition:

For any numbers a, b, and c, $a\left(b+c\right)=ab+ac$.

Calculation:

The given expression is $2\left(x+3\right)$.

By distributive law of multiplication over addition, the given expression can be rewritten as follows.

$\begin{array}{c}2\left(x+3\right)=2\cdot x+2\cdot 3\\ =2x+6\end{array}$

That is, the expression $2\left(x+3\right)$ is equivalent to $2x+6$.

But, the expression $2\left(x+3\right)$ is not equivalent to $2\cdot x+3$.

Thus, the given statement is false.